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Quantum computation in photonic crystals

Dimitris G. Angelakis, Marcelo França Santos, Vassilios Yannopapas, ARTUR K. EKERT

Published Oct 24, 2004• 1 citation
OpenAlex

Abstract

Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We show, that photons confined to photonic crystals, and in particular to highly efficient waveguides formed from linear chains of defects doped with atoms can generate strong non-linear interactions which allow to implement both single and two qubit quantum gates. The simplicity of the gate switching mechanism, the experimental feasibility of fabricating two dimensional photonic crystal structures and integrability of this device with optoelectronics offers new interesting possibilities for optical quantum information processing networks.

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Quantum computers require technologies that offer both sufficient control over coherent quantum phenomena and minimal spurious interactions with the environment. We show, that photons confined to photonic crystals, and in particular to highly efficient waveguides formed from linear chains of defects doped with atoms can generate strong non-linear interactions which allow to implement both single and two qubit quantum gates. The simplicity of the gate switching mechanism, the experimental feasibility of fabricating two dimensional photonic crystal structures and integrability of this device with optoelectronics offers new interesting possibilities for optical quantum information processing networks.
We show how highly non-linear interactions between single photon pulses can be realized in a photonic crystal doped with four level atoms. We describe how two photons, each coupled to a different atomic transition in such atoms, can manifest strong amplitude correlations. In some cases one single photon can trigger the absorption of the other and the device could thus operate as an ultrasensitive nonlinear photon-switch. These effects also allow for the creation of three-partite entangled states of the GHZ form. The realization of a possible GHZ type of non-locality test is investigated. We note the simplicity of the above case over the usual EIT type of schemes requiring the existence of external coupling lasers.
New paradigms for optical physics emerge with lattices of atoms trapped in one and two-dimensional photonic crystals [1-4]. Exemplary experimental platforms include photonic crystal waveguides [5-7] and cavities [8, 9]. Owing to their small optical loss and tight field confinement, these nanoscale dielectric devices are capable of mediating long-range atom-atom interactions using photons propagating in their guided modes. In a complimentary fashion, long-range interactions between photons can be mediated by an underlying lattice of atoms. Such systems have the potential to provide new tools for scalable quantum networks, quantum phases of light and matter, and quantum metrology. However, bringing this future of atom nanophotonics to fruition requires the creation of an interdisciplinary toolkit for the control, manipulation, and interaction of atoms and photons with a complexity and scalability not currently possible. I will give an overview of the theoretical prospects for new physics and review experimental progress in this nascent field at the interfaces of nano-photonics, atomic physics, and quantum optics.
Although practical realisation of a fully functioning quantum computer is still a long way off, recent progress both experimentally and theoretically is paving the way for possible implementations. One of the leading approaches is quantum optics, where photons are used as carriers of quantum information, and are manipulated in both linear and non-linear optical circuits. More recently, advances in integrated quantum photonics are enabling the realisation of compact and stable quantum gates and circuits. This approach provides routes to enhancing the complexity of quantum optic experiments, and ultimately towards the development of advanced quantum technologies. This study presents an overview of recent developments in the field of integrated waveguide quantum circuits. Key building blocks required for the realisation of quantum circuits are presented, and a rudimentary version of Shor's quantum factoring algorithm is demonstrated. Planar waveguide quantum circuits provide a high-performance platform from which quantum technologies and experimental quantum physics using single photons can be developed, and a new generation of quantum information and computing devices can be monolithically integrated onto a single optical chip.
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a four-level system, based on which photon-photon π-phase gates (CONTROLLED-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible, given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
This Thesis is focused on the study of quantum electrodynamics in photonic crystal waveguides. We investigate the interplay between a single quantum dot and the fundamental mode of the photonic crystal waveguide. We demonstrate experimental coupling eciencies for the spontaneous emission into the mode exceeding 98% for emitters spectrally close to the band-edge of the waveguide mode. In addition we illustrate the broadband nature of the underlying eects, by obtaining coupling eciencies above 90% for quantum dots detuned from the band edge by as far as 20nm. These values are in good agreement with numerical simulations. Such a high coupling eciency implies that the system can be considered an articial 1D-atom, and we theoretically show that this system can generate strong photon-photon interaction, which is an essential functionality for deterministic optical quantum information processing. We present the progress towards the experimental demonstration of such a strong photon-photon nonlinearity. We present the rst signatures of resonant transmission in photonic crystal waveguides and discuss some of the encountered diculties and future directions of the experiments. In the nal part of this Thesis we discuss a novel type of photonic crystal waveguide and show its applications for on-chip quantum information processing. This structure was designed for the ecient mapping of two orthogonal circular dipole transitions to dierent propagation paths of the emitted photon, i.e. exhibits chiral quantum-dot-waveguide coupling. Such a structure is ideally suited for a number of applications in quantum information processing and among others we propose an on-chip spin-photon interface, a single photon transistor, and a deterministic cNOT gate.
Compared with other physical platforms for Quantum Information Processing (QIP), photons have the unique advantages of travelling over free-space links or optical fiber with relatively low decoherence and of propagating with minimal coupling to the environment, while also being easily coupled to existing telecommunications technology. The R&D of various single photon and entangled photon generation technologies and the linear-optical implementations of quantum computation and communication are now surveyed and analyzed in a structured manner. We discuss photonic qubit degrees of freedom (polarization, time-bin, path, frequency and Orbital angular momentum), determine sources such as deterministic quantum-dot based sources and probabilistic sources based on spontaneous parametric down conversion (SPDC), and review architectures for Linear Optical Quantum Computation (LOQC), such as the Knill–Laflamme–Milburn (KLM) protocol and measurement-based quantum computation. Building on the density-matrix treatment of biexciton–exciton coherent dynamics in semiconductor quantum dots, we recapitulate the development of two-pulse coherent control schemes for generation and readout of photonic qubits in these systems and how they have been stretched towards optical control of logic gates. A comparative performance framework is established along the lines of source brightness, entanglement fidelity, photon indistinguishability, channel loss and scalability, which is illustrated by simulated performance plots and tabulated against literature numbers. Remaining hurdles in the field regarding issues of photon loss, scalable multiplexing, deterministic two-qubit interaction, and its integration with a quantum memory are highlighted and a perspective is provided on hybrid photonic–matter architectures for fault-tolerant quantum networks.